Dynamical sources in information theory: Fundamental intervals and word prefixes

A quite general model of source that comes from dynamical systems theory is introduced. Within this model, some basic problems of algorithmic information theory contexts are analysed. The main tool is a new object, the generalized Ruelle operator, which can be viewed as a “generating” operator for fundamental intervals (associated to information sharing common prefixes). Its dominant spectral objects are linked with important parameters of the source, such as the entropy, and play a central rôle in all the results.     

Higher order spectral estimation for random fields

This paper is concerned with the nonparametric estimation of the higher order cumulant spectra of vector-valued stationary random fields onZ ^d by smoothing the periodograms, whereZ is the space of integers and the dimensiond1. We derive the asymptotic cumulant properties of the spectral estimates, and consider an application to multidimensional nonlinear systems identification. Numerical examples with simulated data are provided.     

Experimenting with Isabelle in ZF set theory

The theorem prover Isabelle has been used to axiomatise ZF set theory with natural deduction and to prove a number of theorems concerning functions. In particular, the well-founded recursion theorem has been derived, allowing the definition of functions over recursive types (such as the length and the append functions for lists). The theory of functions has been developed sufficiently within ZF to include PP, the theory of continuous functions forming the basis of LCF. Most of the theorems have been derived using backward proofs, with a small amount of automation.The work has been carried out at the Computer Laboratory of the University of Cambridge.     

Towards the implementation of text and discourse theory in computer-assisted textual analysis

Humanities computing (HC) has failed to integrate into its practices many of the key theoretical elements of contemporary text and discourse theory. This has in turn contributed to the marginalization of HC in research and teaching. Outdated theoretical models must be abandoned in order to develop a critical discourse based on the insights of HC. HC projects remain far too attached to micro-analyses and have not developed the theoretical and methodological tools necessary to undertake systemic macro-analyses on the level of discourse. Given that texts are a mixture of determinate and dynamic systems, recent developments in chaos theory may be of help in modelling the interrelationship of these elements at discourse level.Donald Bruce is Associate Professor of Romance Languages at the University of Alberta. His research interests include literary theory, XIXth century French literature, science and literature, and translation. He recently edited an issue ofRecherches Sémiotiques/Semiotic Inquiry on Literature and Ideology and is presently working on a project entitled,The Socio-semiotic Nexus: Jules Vallès and the Discourse of the Commune.     

On the small-scale dynamical behavior of lattice BGK and lattice Boltzmann schemes

In this paper, we report some comparative simulations between lattice BGK and lattice Bolzmann schemes for two-dimensional fluid flows. A quantitative assessment of the validity of the lattice BGK and lattice Bolzmann schemes is presented for the two-dimensional weakly compressibleKolmogorov flow. We use this flow to study the difference of the two schemes at small scales. A lowReynolds (R _e 300) number simulation shows the almost identical energy spectra for both schemes except for the small-scale dynamics of lattice Bolzmann which is more noisy. Because of the intrinsic difficulties of nonlinear stability analysis, we use numerical simulations to investigate which scheme is more stable. It turns out the lattice BGK is more stable. It turns out the lattice BGK is more robust than lattice Bolzmann by increasing theReynolds numbers. Detailed comparison with other methods (e.g., spectral method) remains to be done in the near future.     

Some Comparative Aspects of Equivalence Conditions of Probability Measures Corresponding to Ordinary and Generalized Random Gaussian Fields

Equivalence conditions of probability Gaussian measures corresponding to ordinary and generalized homogeneous random fields are compared and analyzed.     

An approach to evaluation of hierarchical systems performance

An approach to assessment of performance of hierarchical systems with simple subordination is developed with regard to moment characteristics of sequences of random sums. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 70–79, July–August, 2000.     

A theoretical and empirical investigation of multi‐item on‐line auctions

In this paper we explore and analyze the structure of Internet auctions from an analytical and an empirical perspective. Such web‐based auctions are rapidly emerging as a mercantile process of choice in the electronic marketplace. We observe current Internet auctions for one‐time products, such as rapidly aging hardware, and analyze them within the framework of the existing auction theory. While traditional auction theory focuses on single‐item auctions, we observe that a majority of on‐line auctions are multi‐item auctions. A significant contribution of this work is the theoretical derivation of the structure of the winning bids in multi‐item progressive on‐line auctions. Additionally, for comparative purposes, we explore the structural characteristics of alternative multi‐item auction mechanisms proposed in the auction theory. We derive hypotheses based on our analytical results and compare two different types of auction mechanisms. We test the traditional auction theory assumption regarding the homogeneity of bidders and present the first ever empirically derived classification and performance‐comparison of on‐line bidders. We test our hypotheses using real‐world empirical data obtained by tracking a premier web‐based auction site. Statistical analysis of the data indicates that firms may gain by choosing alternative auction mechanisms. We also provide directions for further exploration of this emerging but important dimension of electronic commerce. This revised version was published online in July 2006 with corrections to the Cover Date.